On slow manifolds of chemically reactive systems
- 11 July 2002
- journal article
- research article
- Published by AIP Publishing in The Journal of Chemical Physics
- Vol. 117 (4), 1482-1496
- https://doi.org/10.1063/1.1485959
Abstract
This work addresses the construction of slow manifolds for chemically reactive flows. This construction relies on the same decomposition of a local eigensystem that is used in formation of what are known as Intrinsic Low Dimensional Manifolds (ILDMs). We first clarify the accuracy of the standard ILDM approximation to the set of ordinary differential equations which model spatially homogeneous reactive systems. It is shown that the ILDM is actually only an approximation of the more fundamental Slow Invariant Manifold (SIM) for the same system. Subsequently, we give an improved extension of the standard ILDM method to systems where reaction couples with convection and diffusion. Reduced model equations are obtained by equilibrating the fast dynamics of a closely coupled reaction/convection/diffusion system and resolving only the slow dynamics of the same system in order to reduce computational costs, while maintaining a desired level of accuracy. The improvement is realized through formulation of an elliptic system of partial differential equations which describe the infinite-dimensional Approximate Slow Invariant Manifold (ASIM) for the reactive flow system. This is demonstrated on a simple reaction-diffusion system, where we show that the error incurred when using the ASIM is less than that incurred by use of the Maas-Pope Projection (MPP) of the diffusion effects onto the ILDM. This comparison is further done for ozone decomposition in a premixed laminar flame where an error analysis shows a similar trend.This publication has 29 references indexed in Scilit:
- Low-dimensional manifolds and reduced chemical models for tropospheric chemistry simulationsAtmospheric Environment, 2000
- Direct numerical simulation of turbulent premixed flames using intrinsic low-dimensional manifoldsCombustion Theory and Modelling, 1999
- Efficient calculation of intrinsic low-dimensional manifolds for the simplification of chemical kineticsComputing and Visualization in Science, 1998
- An investigation of the accuracy of manifold methods and splitting schemes in the computational implementation of combustion chemistryCombustion and Flame, 1998
- Comparison of Conventional and Low-Dimensional Manifold Methods to Reduce Reaction MechanismsCombustion Science and Technology, 1997
- Simulation of Laminar Methane-Air Flames using Automatically Simplified Chemical KineticsCombustion Science and Technology, 1996
- Using CSP to Understand Complex Chemical KineticsCombustion Science and Technology, 1993
- The Structure and Stability of Laminar FlamesAnnual Review of Fluid Mechanics, 1993
- Variational sensitivity analysis of a photochemical smog mechanismInternational Journal of Chemical Kinetics, 1985
- The application of centre manifolds to amplitude expansions. I. Ordinary differential equationsJournal of Differential Equations, 1983